Research Papers

Optimization of the Effective Shear Properties of a Bidirectionally Corrugated Sandwich Core Structure

[+] Author and Article Information
Dirk Mohr

Solid Mechanics Laboratory
(CNRS-UMR 7649),
Department of Mechanics,
École Polytechnique,
Palaiseau, France

Here, the adjective “optimal” is used to make reference to the configuration that provides the highest shear modulus among all or a subgroup of configurations considered in this study.

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 13, 2011; final manuscript received March 27, 2012; accepted manuscript posted June 6, 2012; published online October 29, 2012. Assoc. Editor: Vikram Deshpande.

J. Appl. Mech 80(1), 011012 (Oct 29, 2012) (10 pages) Paper No: JAM-11-1232; doi: 10.1115/1.4006941 History: Received July 13, 2011; Revised March 27, 2012; Accepted June 06, 2012

The transverse shear stiffness of a newly-developed all-metal sandwich core structure is determined experimentally and numerically. The core structure is composed of a periodic array of domes which are introduced into an initially flat sheet through stamping. A finite element model of the stamping process is built and validated experimentally. A parametric study is performed to choose the stamping tool geometry such that the resulting core structure provides maximum shear stiffness for a given relative density. It is found that the optimal geometries for relative densities ranging from 0.2 to 0.35 all feature the same dome shape with the same height-to-width ratio. The simulation results also show that the estimated transverse shear strength of the proposed core structure is the same as that of hexagonal honeycombs of the same weight for high relative densities (greater than 0.35), but up to 30% smaller for low relative densities (lower than 0.2). In addition to numerical simulations of a representative unit cell, four-point bending experiments are performed on brazed prototype sandwich beams to validate the computational model.

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Fig. 1

(a) Side view of the four layer sandwich structure, (b) top view of a single core layer

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Fig. 2

(a) Photograph of the stamping tool comprising a male die (part 1) and a female die (part 2); (b) top view, (c) side view of before stamping, (d) side view of during flattening

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Fig. 3

Engineering stress-strain curves for the 0.2 mm thick low carbon steel sheet for loading along different in-plane directions

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Fig. 4

Stamping pressure versus displacement. Note that both curves are initially identical since the theoretical displacement associated with the measure machine stiffness has been added to the simulation result.

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Fig. 5

Side view of a single corrugated layer: comparison of the computed geometry (top) with a scanning electron micrograph of a prototype (bottom)

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Fig. 6

Sequence of computed geometries during the stamping of a unit cell of a single core layer

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Fig. 7

Unit cell model of the sandwich structure for estimating the transverse shear stiffness

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Fig. 8

(a) Macroscopic shear modulus as a function of the height-to-thickness ratio αh; the black crosses represents the simulation results for different stamping tool geometries; (b) cross-sectional views of four selected geometries. The numbered labels indicate the corresponding data points in (a).

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Fig. 9

Optimal configurations for different values of each αh (corresponds to the relative density of the core structure)

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Fig. 10

Influence of the parameters αD and αd on the elastic shear modulus

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Fig. 11

Elastic shear modulus as a function of the relative density for the proposed core structure (solid lines) and hexagonal honeycomb (dashed lines). Note that the shear modulus of the proposed material is the same for both in-plane directions, while the honeycomb stiffness is direction dependent.

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Fig. 12

Four-point bending of wide sandwich beams: (a) photograph of the experimental setup, (b) schematic of the finite element model. The detail depicts a small portion of the deformed finite element mesh.




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